Create 06 - DP With Binary Search Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/19 - Longest Increasing Subsequence/06 - DP With Binary Search Approach.cpp

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+class Solution {
+public:
+    // Helper function to calculate the length of the Longest Increasing Subsequence (LIS)
+    // using a more efficient approach with binary search.
+    int solve(vector<int>& nums) {
+        int n = nums.size(); // Get the size of the array.
+
+        // Create a vector `ans` to store the elements of the current LIS.
+        // It will not necessarily be the actual LIS but will have the same length.
+        vector<int> ans;
+        
+        // Add the first element to the LIS tracker.
+        ans.push_back(nums[0]);
+
+        // Iterate over the rest of the elements in the array.
+        for (int i = 1; i < n; i++) {
+            // If the current element is greater than the last element of `ans`,
+            // it extends the LIS, so add it to the end of `ans`.
+            if (nums[i] > ans.back()) {
+                ans.push_back(nums[i]);
+            } 
+            // Otherwise, replace the smallest element in `ans` that is greater than
+            // or equal to the current element using `lower_bound`.
+            else {
+                int index = lower_bound(ans.begin(), ans.end(), nums[i]) - ans.begin();
+                ans[index] = nums[i];
+            }
+        }
+
+        // The size of the `ans` vector represents the length of the LIS.
+        return ans.size();
+    }
+
+    // Main function to calculate the length of the Longest Increasing Subsequence (LIS).
+    int lengthOfLIS(vector<int>& nums) {
+        int n = nums.size(); // Get the size of the array.
+        return solve(nums); // Call the helper function to solve the problem.
+    }
+};